A formula for the distance of a Toeplitz matrix to the subspace of {e}-circulant matrices is presented, and applications of {e}-circulant matrices to preconditioning of linear systems of equations with a Toeplitz matrix are discussed. Copyright c © 2006 John Wiley & Sons, Ltd. key words: Toeplitz matrix, circulant matrix, {e}-circulant, matrix nearness problem, distance to normality, preconditi...

An n × n matrix D = d[i, j] is said to be circulant, if the entries d[i, j] verifying (j − i) = k mod n, for some k, have the same value (for a survey on circulant matrix properties, see Davis (1979)). A directed (respectively, undirected) graph is circulant, if its adjacency matrix is circulant (respectively, symmetric, and circulant). Similarly, a weighted graph is circulant, if its weighted ...

We combine some basic techniques of linear algebra with some expressions for Toeplitz and circulant matrices and the properties of Gaussian random matrices to estimate the norms of Gaussian Toeplitz and circulant random matrices and their inverses. In the case of circulant matrices we obtain sharp probabilistic estimates, which show that the matrices are expected to be very well conditioned. Ou...

The Circulant Embedding Method (CEM) is a well known technique to generate stationary Gaussian Random Fields (GRF). main idea embed the covariance matrix in larger nested block circulant matrix, whose factorization can be rapidly computed thanks fast Fourier transform (FFT) algorithm. CEM requires extended at least positive semidefinite which proven case if enclosing domain sufficiently large, ...

We first give the style spectral decomposition of a special skew circulant matrix C and then get the style decomposition of arbitrary skew circulant matrix by making use of the Kronecker products between the elements of first row in skew circulant and the special skew circulant C. Besides that, we obtain the singular value of skew circulant matrix as well. Finally, we deal with the optimal back...

The necessary condition for eigenvalue values of a circulant matrix is studied It is then proved that the necessary condition also su ces the existence of a circulant matrix with the prescribed eigenvalue values Introduction An n n matrix C of the form C c c cn cn c c cn cn cn c cn c c cn c is called a circulant matrix As each row of a circulant matrix is just the previous row cycled forward on...

In this paper, we consider the generalized saddle point linear system of equations which is obtained from discretizing the Euler Lagrange equations associated with image debulrring problem. This system is ill-conditioned and is of huge size. Moreover, the (2,2) block of the coefficient matrix of this system contains summation of two terms. One of these terms is a product of a Toepelitz matrix w...

Circulant matrices play a central role in a recently proposed formulation of three-way data computations. In this setting, a three-way table corresponds to a matrix where each “scalar” is a vector of parameters defining a circulant. This interpretation provides many generalizations of results from matrix or vector-space algebra. These results and algorithms are closely related to standard decou...

In this paper, we use the algebra methods, the properties of the r-circulant matrix and the geometric circulant matrix to study the upper and lower bound estimate problems for the spectral norms of a geometric circulant matrix involving the generalized k-Horadam numbers, and we obtain some sharp estimations for them. We can also give a new estimation for the norms of a r-circulant matrix involv...